Published September 25, 2020
| Version v1
Poster
Open
Step-by-step analitical solutions of the Lane-Emden equation with politropic index 0, 1 and 5 using SymPy
Description
Abstract:
In the study of the stellar structures, some models arises to explain their interior dynamics and surface consequences (measurable in the laboratory), the Lane-Emden equation provides us with a detailed explanation of the astrophysical properties of these stars based on newtonian self-gravitating, spherically symmetric and polytropic fluid. We present a revisited step by step solution for the well known cases for politropic index n=0 and n=1, and all real solutions for n=5 in terms of Jacobian and Weierstrass elliptic functions. All the calculus are performed using Sympy.
Notes
A poster presentation for XIX Meeting of Physics in Peru. Video and more presentations are in:this link: https://indico.uni.edu.pe/event/85/contributions/337/
Files
01_polytropic_index_0.ipynb
Additional details
References
- S. Chandrasekhar. An Introduction to the Study of Stellar Structure. Dover Publications, 201
- Aaron Meurer, Christopher P. Smith, Mateusz Paprocki, Ondˇrej Certík, Sergey B. Kirpichev, Matthew ˇ Rocklin, AMiT Kumar, Sergiu Ivanov, Jason K. Moore, Sartaj Singh, Thilina Rathnayake, Sean Vig, Brian E. Granger, Richard P. Muller, Francesco Bonazzi, Harsh Gupta, Shivam Vats, Fredrik Johansson, Fabian Pedregosa, Matthew J. Curry, Andy R. Terrel, Štˇepán Rouˇcka, Ashutosh Saboo, Isuru Fernando, Sumith Kulal, Robert Cimrman, and Anthony Scopatz. Sympy: symbolic computing in python. PeerJ Computer Science, 3:e103, January 201
- Patryk Mach. All solutions of the n = 5 laneemden equation. Journal of Mathematical Physics, 53(6):062503, Jun 2012.